## Linear Operators: General theory |

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Page 511

9 . Exercises 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of

the product Poex Yz , where Yv = Y , under the mapping T → P8XTx . Show that

the strong topology of

9 . Exercises 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of

the product Poex Yz , where Yv = Y , under the mapping T → P8XTx . Show that

the strong topology of

**operators**in B ( X , Y ) is identical with the usual product ...Page 540

Nelson Dunford.

space X . Weakly compact

] . A very incisive discussion of weakly compact

...

Nelson Dunford.

**operator**and the**operator**mapping into a weakly completespace X . Weakly compact

**operators**from C [ 0 , 1 ] to X were treated by Sirvint [ 3] . A very incisive discussion of weakly compact

**operators**with domain C ( S ) was...

Page 838

13.8 (223) Borel-Stieltjes measure, (142) Bound, of an

partially ordered set, 1.2.3 (4) in the (extended) real number system, (3)

Boundary, of a set, 1.4.9 (11) Bounded, essentially (or /i-essentially ), definition, III

.

13.8 (223) Borel-Stieltjes measure, (142) Bound, of an

**operator**, II.3.5 (60) in apartially ordered set, 1.2.3 (4) in the (extended) real number system, (3)

Boundary, of a set, 1.4.9 (11) Bounded, essentially (or /i-essentially ), definition, III

.

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero